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Unformatted text preview: a) Why the model is known as a linear probability model (LPM)? Comment on the interpretation of 1. The model is known as a linear probability model (LPM) because it consist a binary dependent variable namely ecobuy and the response probability is linear in the parameters. In the LPM, 1 is interpreted as changes in the probability of success (y=1 where family are buying ecolabeled apples) given a one dollar increase to the price of ecolabeled apples, holding all other factors fixed. b) Suppose that MLR14 hold for the model when all variables are correctly measured. Further suppose that one regressor, faminc, is measured with an additive error and the error is uncorrelated with the truth faminc* . How would the OLS estimator of, say, 1 be affected by the measurement error and why? Additive error occur as a result of over specifying the regression model however the measurement error will not cause bias or inconsistency to the intercept and OLS estimators of say 1 because it satisfies MLR14. But since it violates MLR 5 homoskedasticity assumption implying to the presence of heteroskedasticity, it will have undesirable impact will be on the variances of the OLS estimators making it asymptotically inefficient where the variance could either be too large or too small thus impacting on the standard errors making the usual construction of confidence levels, t and F statistics no longer valid. c) Estimate the model, using OLS, and interpret the estimate of 5. Ecobuy= 0.424  0.803ecoprc + 0.719regprc + 0.00055faminc + 0.024hhsize + 0.025educ  0.00050age (.165) (.109) (.132) (.00053) (.013) (.008) (.00125) n= 660 R2= 0.110 Educ appears to have most important effect among the nonprice variable factors. So an extra year of schooling implies an increase of 0.025 in the estimated probability of buying ecolabeled apples. This suggests that more highly educated people will be more inclined to purchase apples that are environmentally friendly. d) Find het.robust standard errors and compare these with the usual OLS standard errors. Ecobuy= 0.424  0.803ecoprc + 0.719regprc + 0.00055faminc + 0.024hhsize + 0.025educ  0.00050age (.165) (.109) (.132) (.00053) (.013) (.008) (.00125) OLS standard errors [.167] [.105] [.130] [.00052] [.012] [.008] [.00126] Hetrobust standard errors n= 660 R2= 0.110 It can be seen that the het robust standard errors can be either larger (age), same (educ) or smaller (ecoprc, regprc, faminc and hhsize) than the usual standard errors. For the variable age, the hetrobust standard error was greater than the OLS standard error by 0.00001, for variable educ the hetrobust standard error was the same to the OLS standard error when rounded to 3 decimal places, for ecoprc the hetrobust standard error was less than the OLS standard error by 0.004 probably the largest relative change in standard errors in this example, for regprc the hetrobust standard error was less than the OLS standard error by 0.002, for faminc the hetrobust standard error was less than the OLS standard error by 0.00001 and for the variable hhsize faminc the hetrobust standard error was less than the OLS standard error by 0....
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